Question

Question

Write  in trigonometric form and find their product. 

Answer 1

Step 1:

The complex numbers are and .

The polar form of a complex number  is .

Where , and .

Here  is the magnitude of the complex number and  is argument of .

Compare the complex number with .

Here and .

Magnitude of :

.

Substitute , and in and .

and

and .

Since the cosine function is negative and sine function is positive, lies in second quadrant.

The angle satisfies both the conditions is .

Substitute and in trigonometric form.

.

The trigonometric form of is .

Step 2:

Compare the complex number with .

Here and .

Magnitude of :

.

Substitute , and in and .

and

and .

Since both the trigonometric functions are negative, lies in third quadrant.

The angle satisfies both the conditions is .

Substitute and in trigonometric form.

.

The trigonometric form of is .

Solution:

The trigonometric form of is .

The trigonometric form of is .

Answer 2

The trigonometric form of is .

The trigonometric form of is .

Product of complex numbers in trigonometric form : .

.